Transactions of the Korean Nuclear Society Autumn Meeting Goyang, Korea, October 24-25, 2019

Thermal-Hydraulics Evaluation Program Development for U-type Steam Generator of APR1400

Kunwoo Yi a, Seonghoon Hwanga, Kyongin Jua, Seongchan Parka aKEPCO Engineering and Construction Company, 989-113 daedukdaero, Yuseong-gu, Daejeon, Korea *Corresponding author: [email protected]

1. Introduction

The APR1400 steam generators represent the uprated and evolutionary design from the OPR1000 operating steam generators. Reactor enters the inlet plenum through the primary inlet nozzle, flows up through the tube sheet and U-type tube, and returns through the tube sheet to the outlet plenum and exits through the two outlet nozzles. Feed water enters the region at the tube sheet on the cold leg side of the tube bundle. Above the flow distribution plate, feed water flows upward in axial counter flow, being heated by forced to near saturation conditions at the top of the economizer. by nucleate boiling occurs in the as the secondary fluid flows upward continually increasing in steam quality. In most previous studies, a steam generator is designed to be optimized to remove heat and to produce steam vapor. Because of its importance, theoretical and experimental researches have been performed on forced convection Fig. 1 Schematic diagram of energy balance in each boiling heat transfer [1, 2]. cotinuum.

The purpose of this study is to establish a thermal Typical thermal sizing is related to the calculations hydraulic evaluation program for evaluating operating required for the heat transfer area to meet specified parameters of steam generator in order to develop an conditions [3]. Fig. 1 is a schematic diagram for NSSS (Nuclear Steam Supply System) thermal calculating each heat transfer area. In general, it is performance evaluation program for assessing thermal possible to calculate the heat transfer of each area by power, operating characteristics of RCS (Reactor applying the energy equations for the three physical Coolant system) and steam generator, and so on. continuums. The analytical modeling of a steam generator is employed based on the empirical correlation equations -primary side and theory. Q  m p (H pin  H pout )

2. Methods and Results -tube side

 Thot Tsat  Q  UATm  UAi (Thot Tcold ) / ln  Heat transfer is calculated independently in the T T convection and boiling region. The size of the tube  cold sat  length is calculated for a given number of tubes, -secondary side primary temperature and steam pressure, and the thermal performance of the steam generator is estimated Q  ms (H s,in  H s,out ) for a fixed number of tubes and tube length, primary temperature or steam pressure. The axial-flow The overall heat transfer coefficient can be economizer region and evaporator region require calculated as follows. separate analyses due to the different modes of heat transfer.  1 D D D 1  1 U    o  o ln o      h p Di 2kw Di hs  2.1 Theoretical calculation of steam generator

Transactions of the Korean Nuclear Society Autumn Meeting Goyang, Korea, October 24-25, 2019

Here, Q , M , H , U , A , D and T are thermal power, 2  ''  3 q  mass flow rate, , overall heat transfer, heat   ho  transfer area, tube diameter and temperature  1   1    2  respectively. And subscripts p , s , o , i and w C Pr1.7 sf l     represent primary side, secondary side, outer wall, inner  l hlv  g(l  v )     wall and tube wall respectively.

All other parameters are usually fixed at the specified '' value. In most thermal-hydraulics performance Here, T , q , hlv , C p ,  ,  , Csf are temperature, calculations, the heat transfer area is fixed and the heat flux, of vaporization, specific heat, variable of interest is the inlet or outlet of primary viscosity, interfacial tension and constant value for temperature or secondary pressure. Even though the different liquid-surface combination respectively, and s total heat load and various thermal hydraulic values of l and v of subscript are liquid and vapor. The value of the steam generator are known, the heat load provided Csf is applied to 0.013 in the thermal-hydraulics to the evaporator and economizer regions cannot be defined explicitly. This requires an iterative solution. evaluation program [4, 5].

The assumptions applied to the thermal-hydraulics 2.2 Evaluation of Thermal Performance evaluation program of steam generator are as follows. Table I: Steam Generator Parameters on APR1400 (a) Steady state conditions Symbo Input Parameters Value (b) The heat transfer model considers the average l primary flow per tube for the average tube length Core/SG Thermal Rating Pcore 2000MWt (c) Nucleate boiling is the mode of heat transfer in Primary side the evaporator region P (d) The secondary side temperature is constant at Operating pressure p 15.5MPa T saturation conditions throughout the evaporator Primary inlet temperature p,inlet 323.9oC (e) Heat transfer in the economizer is by forced convection with axial counter-flow T Primary outlet temperature p,outlet 290.6oC (f) The pinch temperature is defined as the point where the economizer and evaporator heat flux is the Primary mass flowrate m p 37.78 106 kg/hr same at the interface of the economizer and the Secondary side evaporator. Saturation pressure Ps 6.9MPa o The boiling equation of the evaporator can use the Saturation temperature Tsat 285.0 C

Rohsenow correlation [4]. The difference between the Feedwater temperature T feed 232.2oC wall and the internal saturation temperature and the m 6 Rohsenow correlation equation are defined as, Secondary mass flowrate s 4.07 10 kg/hr

Table 1 shows the typical steam generator operating Tsat  Tw Tsat parameters under normal operating conditions. The  1  1 2  ''  3 1.7 1     sizing of the steam generator calculates the length of the Tsat  q  Csf Prl        lhlv  g(l  v)   tube according to the thermal power, the primary flow,   the primary temperature, and the secondary guaranteed steam pressure. The heat transfer coefficient in the Nusselt number was defined as, On the contrary, the developed steam generator thermal hydraulic evaluation program can q'' independently predict the primary side temperature ho  Tw Tsat (Pl ) condition and the secondary side saturation pressure with the minimum operation data obtained on the primary side or the secondary side, with the number of Here Tw is the surface temperature and Pl is the tubes and the average length as fixed variables. When ambient temperature. Therefore, the heat transfer the RCS flow rate, saturation pressure of steam coefficient ( h ) can be expressed as, o generator, main feed flow rate, and feed water temperature are applied to the performance evaluation program, the primary outlet temperature is 289.6 oC and the primary inlet temperature is 323.1 oC. This error is estimated to be 0.34% for the primary outlet Transactions of the Korean Nuclear Society Autumn Meeting Goyang, Korea, October 24-25, 2019

temperature and 0.25% for the primary inlet temperature. Also, if the RCS flow rate, primary side temperature, secondary side main water flow, and main water temperature are applied to the performance variable program, the steam generator pressure is estimated to be 7.0 MPa, 1.54% higher than the design variable.

The thermal-hydraulics evaluation program of steam generator can be utilized to predict steam generator thermal performance related variables by evaluating the applicable operating variables.

3. Conclusions

The developed thermal-hydraulics evaluation program of steam generator predicted approximately 0.3% lower primary side temperature and the steam generator pressure was estimated to be approximately 1.5% high. The evaluation program is acceptable for estimating operation parameters of the currently operating power plant can be used to evaluate the operating variables of the power plant.

REFERENCES

[1] Jose Zambrana, et al, Vertical tube length calculation based on available heat transfer coefficient expression for the subcooled flow boiling region, Applied Thermal Engineering, 28, pp.499-513, 2008. [2] Masahiro Osakabe, Thermal-Hydraulic Study of Integrated Steam Generator in PWR, Journal of Nuclear Science and Technology, Vol. 26, pp. 286-294, 1989. [3] Frank P. Incropera, Introduction to Heat Transfer, 5th Edition, John Wiley&Sons, 2007. [4] A.E. Bergles, W.M. Rohsenow, The determination of forced-convection surface-boiling heat transfer, Journal of Heat Transfer, 86, pp. 365-372, 1964 [5] Van P. Carey, Liquid-Vapor Phase-Change Phenomena, 1992.